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D.7.3.13 ReynoldsOperator
Procedure from library rinvar.lib (see rinvar_lib).
- Usage:
- ReynoldsOperator(G, action [, opt]); ideal G, action; int opt
- Purpose:
- compute the Reynolds operator of the group G which acts via 'action'
- Return:
- polynomial ring R over a simple extension of the ground field of the
basering (the extension might be trivial), containing a list
'ROelements', the ideals 'id', 'actionid' and the polynomial 'newA'.
R = K(a)[s(1..r),t(1..n)].
- 'ROelements' is a list of ideals, each ideal represents a
substitution map F : R -> R according to the zero-set of G
- 'id' is the ideal of G in the new ring
- 'newA' is the new representation of a' in terms of a. If the
basering does not contain a parameter then 'newA' = 'a'.
- Assume:
- basering = K[s(1..r),t(1..n)], K = Q or K = Q(a') and minpoly != 0,
G is the ideal of a finite group in K[s(1..r)], 'action' is a linear
group action of G
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